Jaume Carot

University of the Balearic Islands | UIB · Department of Physics

Citation: Herrera, L.; Di Prisco, A.; Ospino, J.; Carot, J. Quasi-Hyperbolically Symmetric γ-Metric. Entropy 2023, 25, 1338. https:// Abstract: We carry out a systematic study on the motion of test particles in the region inner to the naked singularity of a quasi-hyperbolically symmetric γ-metric. The geodesic equations are written and analyzed in...

We carry out a systematic study on the motion of test particles in the region inner to the naked singularity of a quasi–hyperbolically symmetric γ-metric. The geodesic equations are written and analyzed in detail. The obtained results are contrasted with the corresponding results obtained for the axially symmetric γ-metric, and the hyperbolically s...

It is shown that exact spherically symmetric solutions to Einstein’s field equations exist such that, over an open region of the spacetime, they are singularity free, satisfy the dominant energy condition, represent elastic matter with a well-defined constitutive function, and are such that elastic perturbations propagate causally. Two toy models a...

It is shown that exact spherically symmetric solutions to Einstein's Field Equations exist such that, over an open region of the spacetime, they are singularity free, satisfy the dominant energy condition, represent elastic matter with a well defined constitutive function, and are such that elastic perturbations propagate causally. Two toy-models a...

A recently introduced concept of complexity for relativistic fluids is extended to the vacuum solutions represented by the Bondi metric. A complexity hierarchy is established, ranging from the Minkowski spacetime (the simplest one) to gravitationally radiating systems (the more complex). Particularly interesting is the possibility to differentiate...

A recently introduced concept of complexity for relativistic fluids is extended to the vacuum solutions represented by the Bondi metric. A complexity hierarchy is established, ranging from the Minkowski spacetime (the simplest one) to gravitationally radiating systems (the more complex). Particularly interesting is the possibility to differentiate...

We carry on a systematic study of the physical properties of axially symmetric fluid distributions, which appear to be geodesic, shearfree, irrotational, nondissipative, and purely electric, for the comoving congruence of observers, from the point of view of the tilted congruence. The vanishing of the magnetic part of the Weyl tensor for the comovi...

We carry on a systematic study of the physical properties of axially symmetric fluid distributions, which appear to be geodesic, shear--free, irrotational, non--dissipative and purely electric, for the comoving congruence of observers, from the point of view of the tilted congruence. The vanishing of the magnetic part of the Weyl tensor for the com...

We report a study on axially and reflection symmetric dissipative fluids, just after its departure from hydrostatic and thermal equilibrium, at the smallest time scale at which the first signs of dynamic evolution appear. Such a time scale is smaller than the thermal relaxation time, the thermal adjustment time and the hydrostatic time. It is obtai...

We report a study on axially and reflection symmetric dissipative fluids, just after its departure from hydrostatic and thermal equilibrium, at the smallest time scale at which the first signs of dynamic evolution appear. Such a time scale is smaller than the thermal relaxation time, the thermal adjustment time and the hydrostatic time. It is obtai...

Using a framework based on the $1+3$ formalism we carry out a study on axially and reflection symmetric dissipative fluids, in the quasi--static regime. We first derive a set of invariantly defined "velocities", which allow for an inambiguous definition of the quasi--static approximation. Next we rewrite all the relevant equations in this aproximat...

Using a framework based on the 1+3 formalism we carry out a study on axially and reflection symmetric perfect and geodesic fluids, looking for possible models of sources radiating gravitational waves. Therefore, the fluid should be necessarily shearing, for otherwise the magnetic part of the Weyl tensor vanishes, leading to a vanishing of the super...

Spacetimes which are conformally related to reducible 1+3 spacetimes are considered. We classify these spacetimes according to the conformal algebra of the underlying reducible spacetime, giving in each case canonical expressions for the metric and conformal Killing vectors, and provide physically meaningful examples.

The Einstein field equations are derived for a static cylindrically symmetric spacetime with elastic matter. The equations can be reduced to a system of two nonlinear ordinary differential equations and we present analytical and numerical solutions satisfying the dominant energy conditions. Furthermore, we show that the solutions can be matched at...

A complete classification of locally spherically symmetric four-dimensional Lorentzian spacetimes is given in terms of their local conformal symmetries. The general solution is given in terms of canonical metric types and the associated conformal Lie algebras. The analysis is based upon the local conformal decomposition into 2+2 reducible spacetime...

We analyze the properties of the tilted Szekeres spacetime, i.e. the version of such spacetime as seen by a congruence of observers with respect to which the fluid is moving. The imperfect fluid and the kinematical variables associated to the four-velocity of the fluid assigned by tilted observers are studied in detail. As it happens for the case o...

We consider a static cylindrically symmetric spacetime with elastic matter and study the matching problem of this spacetime with a suitable exterior. For the exterior, we take the Levi-Civita spacetime and its generalization including a cosmological constant, the Linet-Tian spacetime. We show that the matching is only possible with the Linet-Tian s...

In the context of relativistic elasticity it is interesting to study axially symmetric space-times due to their significance in modeling neutron stars and other astrophysical systems of interest. To approach this problem, here, a particular class of these space-times is considered. A cylindrically symmetric elastic space-time configuration is studi...

Given a space-time and a continuous medium with elastic properties described by a 3-dimensional material space, one can ask whether they are compatible in the context of relativistic elasticity. Here a non-static, spherically symmetric spacetime metric is considered and we investigate the conditions for that metric to correspond to different 3-dime...

It is shown that, given an analytic Lorentzian metric on a 4-manifold, gab, which admits two Killing vector fields, there exists a local deformation law etaab = a gab + b Hab, where Hab is a two-dimensional projector, such that etaab is flat and admits the same Killing vectors. We also characterize the particular case when the projector Hab coincid...

It is shown that, given an analytic Lorentzian metric on a 4-manifold, gab, which admits two Killing vector fields, it exists a local deformation law ηab = agab + b Hab, where Hab is a 2-dimensional projector, such that ηab is flat and admits the same Killing vectors.

The relativistic theory of elasticity is reviewed within the spherically symmetric context with a view towards the modelling of star interiors possessing elastic properties such as the ones expected in neutron stars. Emphasis is placed on generality in the main sections of the paper, and the results are then applied to specific examples. Along the...

We consider extensions of Lemaitre-Tolman-Bondi (LTB) spacetimes to the dissipative case. For doing that we previously carry out a systematic study on LTB. This study is based on two different aspects of LTB. On the one hand, a symmetry property of LTB will be presented. On the other hand, the description of LTB in terms of some fundamental scalar...

The relativistic theory of elasticity is reviewed within the spherically symmetric context with a view towards the modeling of star interiors possessing elastic properties such as theones expected in neutron stars. Emphasis is placed on generality in the main sections of the paper, and the results are then applied to specific examples. Along the wa...

We calculate the instantaneous proper radial acceleration of test particles (as measured by a locally defined Lorentzian observer) in a Weyl spacetime, close to the horizon. As expected from the Israel theorem, there appear some bifurcations with respect to the spherically symmetric case (Schwarzschild), which are explained in terms of the behaviou...

The flat deformation theorem states that given a semi‐Riemannian analytic metric g on a manifold, locally it can always be written in terms of a semi‐Riemannian flat metric η, a two‐form F and a scalar function c fulfilling a prescribed scalar constraint, say Ψ(c,F,x) = 0. Here we show that if the original metric g admits a Killing vector, then...

The submersion of a 4-dimensional semi-Riemannian manifold having a 1-parameter group of isometries onto the quotient manifold is studied. It is applied to prove that a 4-dimensional Lorentzian metric admitting such a group can be deformed into a flat metric having the same isometries.

We show that the vorticity appearing in stationary vacuum spacetimes is always related to the existence of a flow of superenergy on the plane orthogonal to the vorticity vector. This result, together with the previously established link between vorticity and superenergy in radiative (Bondi-Sachs) spacetimes, strengthens further the case for this la...

These are exciting times for any scientist working on relativity, cosmology and/or gravitation. The contents of this volume correspond to the 2006 Spanish Relativity Meeting, held at Palma de Mallorca. Since the 2005 meeting, which took place in Oviedo, many important developments have taken place in this area of knowledge. Take for instance the nu...

The consistency of the constraint with the evolution equations for spatially inhomogeneous and irrotational silent (SIIS) models of Petrov type I, demands that the former are preserved along the timelike congruence represented by the velocity of the dust fluid, leading to new nontrivial constraints. This fact has been used to conjecture that the re...

We calculate the vorticity of world--lines of observers at rest in a Bondi--Sachs frame, produced by gravitational radiation, in a general Sachs metric. We claim that such an effect is related to the super--Poynting vector, in a similar way as the existence of the electromagnetic Poynting vector is related to the vorticity in stationary electrovacu...

A study covering some aspects of the Einstein--Rosen metric is presented. The electric and magnetic parts of the Weyl tensor are calculated. It is shown that there are no purely magnetic E--R spacetimes, and also that a purely electric E--R spacetime is necessarily static. The geodesics equations are found and circular ones are analyzed in detail....

The electric and the magnetic part of the Weyl tensor, as well as the invariants obtained from them, are calculated for the Bondi vacuum metric. One of the invariants vanishes identically and the other only exhibits contributions from terms of the Weyl tensor containing the static part of the field. It is shown that the necessary and sufficient con...

We discuss certain general features of type B warped spacetimes which have important consequences on the material content they may admit and its associated dynamics. We show that, for warped B spacetimes, if shear and anisotropy are nonvanishing, they have to be proportional. We also study some of the physics related to the warping factor and of th...

An almost-stationary gauge condition is proposed with a view to Numerical Relativity applications. The time lines are defined as the integral curves of the timelike solutions of the harmonic almost-Killing equation. This vector equation is derived by a variational principle, by minimizing the deviations from isometry. The corresponding almost-stati...

The existence of a Conformal Vector Field (CVF) is studied in the important class of warped manifolds of arbitrary dimension generalizing in this way the corresponding results of the four dimensional geometries. As a concrete example we apply the geometric results in the case of brane-world scenarios when the bulk geometry admits a hypersurface ort...

An invariant characterization of double warped space–times is given in terms of Newman–Penrose formalism and a classification scheme is proposed. A detailed study of the conformal algebra of these space–times is also carried out and some remarks are made on certain classes of exact solutions. © 2003 American Institute of Physics.

Inhomogeneous G 2 solutions whose material content can be modelled by a scalar field are considered with a view towards their application as cosmological models. Some generic features of these spacetimes are reviewed and discussed, and dynamical systems theory is used to analyse the qualitative behaviour of this class of spacetimes; giving special...

We define inheriting conformal Killing vectors for null fluid spacetimes and find the maximum dimension of the associated inheriting Lie algebra. We show that for non-conformally flat null fluid spacetimes, the maximum dimension of the inheriting algebra is seven and for conformally flat null fluid spacetimes the maximum dimension is eight. In addi...

Spacetimes which are conformal to 2 + 2 reducible spacetimes are considered. We classify them according to their conformal algebra, giving in each case explicit expressions for the metric and conformal Killing vectors, and providing physically meaningful examples.

Scalar field spacetimes are considered with a view towards their applications in cosmology. Some results existing in the literature are reviewed and some new results are proved concerning scalar field spacetimes in general and inhomogeneous G2 cosmological models in particular.

Scalar field spacetimes are considered with a view towards their applications in cosmology. Some results existing in the literature are reviewed and some new others are proven concerning inhomogeneous G2 cosmological models. Dynamical systems theory is used to analyze the qualitative behavior of certain families of solutions.

The definition of axial symmetry in general relativity is reviewed, and some results concerning the geometry in a neighbourhood of the axis are derived. Expressions for the metric are given in different coordinate systems, and emphasis is placed on how the metric coefficients tend to zero when approaching the axis.

Space-times admitting a 3-dimensional Lie group of conformal motions $C_3$ acting on null orbits are studied. Coordinate expressions for the metric and the conformal Killing vectors (CKV) are then provided (irrespectively of the matter content) and all possible perfect fluid solutions are found, although none of them verifies the weak and dominant...

Space-times admitting an $r$-parameter Lie group of homotheties are studied for $r > 2$ devoting a special attention to those representing perfect fluid solutions to Einstein's field equations.

Perfect fluid space-times admitting a three-dimensional Lie group of conformal motions containing a two-dimensional Abelian Lie subgroup of isometries are studied. Demanding that the conformal Killing vector be proper (i.e., not homothetic nor Killing), all such space-times are classified according to the structure of their corresponding three-dime...

Spacetimes admitting a similarity group are considered. Amongst them, special attention is given to the 3-parameter ones. A classification of such spacetimes is given based on the Bianchi type of the similarity group $H_3$, and the general form of the metric is provided in each case assuming the orbits are non-null. Comment: Latex 17 pages. Error c...

Perfect fluid space-times admitting a three-dimensional Lie group of conformal motions containing a two-dimensional Abelian Lie subgroup of isometries are studied. Demanding that the conformal Killing vector be proper (i.e., not homothetic nor Killing), all such space-times are classified according to the structure of their corresponding three-dime...

The standard definition of cylindrical symmetry in General Relativity is reviewed. Taking the view that axial symmetry is an essential pre-requisite for cylindrical symmetry, it is argued that the requirement of orthogonal transitivity of the isometry group should be dropped, this leading to a new, more general definition of cylindrical symmetry. S...

Spherically symmetric spacetimes representing a perfect fluid coupled to an electromagnetic field are considered in full generality. It is shown that the Hall current is necessarily zero and that the four-current contains, in general, both a convection and a conduction term in the case of a non-null electromagnetic field, whereas it vanishes necess...

An invariant characterization of warped spacetimes is given and a classification scheme for them is proposed. Some results on the curvature structure (Petrov and Segre types of the Weyl and Ricci tensors) are given and a thorough study of the isometry group that each class of warped spacetime may admit is carried out.

A brief summary of results on homotheties in general relativity is given, including general information about spacetimes admitting anr-parameter group of homothetic transformations for r>2, as well as some specific results on perfect fluids. Attention is then focused on inhomogeneous models, in particular on those with a homothetic group (acting mu...

The whole family of generalised soliton solutions of the Weyl class for Einstein's equations in vacuum is considered. A classification scheme for the distinct types of metrics belonging to this family is given and emphasis is placed on the asymptotically flat solutions. The physical interpretation of the occurring parameters is also briefly conside...

Department of Mathematical Sciences, University of Aberdeen, Edward Wright Building, Dunbar Street, Aberdeen AB9 2TY, UK Department de Fisica, Universitat de les Illes Balears, E-07071 Palma de Mallorca, Spain

Initial data corresponding to spacetimes containing black holes are considered in the time symmetric case. The solutions are obtained by matching across the apparent horizon different, conformally flat, spatial metrics. The exterior metric is the vacuum solution obtained by the well known conformal imaging method. The interior metric for every blac...

Space-times admitting a 3-dimensional Lie group of conformal motions $C_3$ acting on null orbits are studied. Coordinate expressions for the metric and the conformal Killing vectors (CKV) are provided (irrespectively of the matter content) and then all possible perfect fluid solutions are found, although none of these verify the weak and dominant e...

We present the general structure of proper Ricci Collineations (RC) for type B warped space-times. Within this framework, we give a detailed description of the most general proper RC for spherically symmetric metrics. As examples, static spherically symmetric and Friedmann-Robertson-Walker space-times are considered.

We present a counter example to a theorem given by Amir et al. [J. Math. Phys. 35, 3005–3012 (1994)]. We also comment on a misleading statement of the same reference. © 1996 American Institute of Physics.

A recent result by Haggag and Hajj-Boutros is reviewed within the framework of self-similar space-times, extending, in some sense, their results and presenting a family of metrics consisting of all the static spherically symmetric perfect fluid solutions admitting a homothety.

Matter collineations, as a symmetry property of the energy-momentum tensor Tab, are studied from the point of view of the Lie algebra of vector fields generating them. Most attention is given to space–times with a degenerate energy-momentum tensor. Some examples of matter collineations are found for dust fluids (including Szekeres’s space–times), a...

The existence of an affine vector field in an Einstein-Maxwell space-time is discussed. We first consider the non-null electromagnetic field case, and show that there are no solutions of the Einstein-Maxwell equations admitting a proper affine collineation. In the case of a null electromagnetic field case, we characterize all the possible solutions...

Some basic concepts about curvature collineations are reviewed and the existing results on this topic are applied to the case of perfect fluids, giving a characterization of those amongst them which admit proper curvature collineations.

Rigidly rotating perfect fluids admitting two Killing vectors ξ (stationarity), η (axial symmetry), and a proper conformal Killing vector K are studied. The three‐dimensional Lie algebra [ξ,η]=0, [ξ,K]=a4K, [η,K]=a3K, a32+a42≠0 is considered. It is shown that under these assumptions there are no space‐times satisfying Einstein’s field equations.

The effects of surface phenomena on the evolution of the boundary of some general relativistic compact objects are analyzed. In particular it is shown that for a subfamily of these objects which expand permanently in the absence of surface phenomena, the presence of arbitrarily small surface tension leads to bounded configurations.

The problem of entropy production in near-equilibrium situations and their evolution towards a state of thermodynamic equilibrium is considered in the cosmological context. A physically realistic model (i.e., satisfying the energy conditions) describing such a situation is constructed. From a few hypotheses and considerations, it is seen that the m...

Space-times admitting special conformai Killing vectors are studied, and some results, already existing in the literature are reviewed from a different point of view. A classification scheme for those space-times whose associated conformai factor has a non-null gradient is presented in terms of their group of isometries, giving in each case the exp...

It is shown that viscous fluid solutions can be obtained by performing conformal transformations of vacuum solutions of Einstein’s field equations. The solutions obtained by such a procedure can be matched, under certain conditions, to their respective original vacuum metrics.

The problem of the centre of mass in a Hamiltonian relativistic system of directly interacting point particles is analysed. A proof is given of the nonexistence of three centre-of-mass canonical co-ordinates which are covariant and depend only on the generating functions of the Poincaré algebra. Finally, the latter condition is given up and a solut...

An example of the equivalence between a perfect fluid and a viscous fluid is presented, showing that the Schwarzschild interior solution obtained from a perfect fluid can also be derived from a viscous fluid with heat conduction. The equivalence between a scalar field and a viscous fluid is investigated, showing that under certain circumstances, bo...

Spacetimes admitting a similarity group are considered. Amongst them, special atten- tion is given to the 3-parameter ones. A classification of such spacetimes is given based on the Bianchi type of the similarity group H3, and the general form of the metric is provided in each case assuming the orbits are non-null.